共查询到18条相似文献,搜索用时 109 毫秒
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研究了多目标优化问题的近似解. 首先证明了多面体集是 co-radiant集,并证明了一些性质. 随后研究了多面体集下多目标优化问题近似解的特殊性质. 相似文献
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主要研究了两类近似凸集的关系和性质.首先,举例说明两类近似凸集没有相互包含关系.其次,在近似凸集(nearly convex)条件下,证明了在一定条件下函数上图是近似凸集与凸集的等价关系.同时,考虑了近似凸函数与函数上图是近似凸集的等价刻画、近似凸函数与函数水平集是近似凸集的必要性,并用例子说明近似凸函数与函数水平集是近似凸集的充分性不成立.最后,基于近似凸函数和拟凸函数的概念,给出了近似拟凸函数的概念并研究了近似拟凸函数与水平集是近似凸集的等价刻画. 相似文献
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在局部凸空间中考虑集值优化问题(VP)在强有效解意义下的Kuhn-Tucker最优性条件.在近似锥.次类凸假设下利用择一性定理得到了(VP)取得强有效解的必要条件,利用基泛函的性质给出了(VP)取得强有效解的充分条件,最后给出了一种与(VP)等价的无约束规划。 相似文献
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在局部凸空间中考虑约束集值优化问题(VP)在超有效解意义下的Lagrange最优性条件.在近似锥-次类凸假设下,利用择一性定理得到了(VP)取得强有效解的必要条件,利用超有效解集的性质及超有效解的定义给出了(VP)取得超有效解的充分条件,最后给出了一种与(VP)等价的无约束规划. 相似文献
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H. Mohebi 《Journal of Global Optimization》2013,55(3):521-538
In this paper, we investigate abstract convexity of non-positive increasing and radiant (IR) functions over a topological vector space. We characterize the essential results of abstract convexity such as support set, subdifferential and polarity of these functions. We also give some characterizations of a certain kind of polarity and separation property for non-convex radiant and co-radiant sets. 相似文献
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In this paper, we present an extension for non-negative increasing and co-radiant (ICR) functions over a topological vector
space. We characterize the essential results of abstract convexity such as support set, subdifferential and polarity of these
functions. We also give some characterizations of a certain kind of polarity and separation property for non-convex radiant
and co-radiant sets. 相似文献
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《Operations Research Letters》2019,47(3):185-189
We consider the augmented Lagrangian method (ALM) for constrained optimization problems in the presence of convex inequality and convex abstract constraints. We focus on the case where the Lagrangian sub-problems are solved up to approximate stationary points, with increasing accuracy. We analyze two different criteria of approximate stationarity for the sub-problems and we prove the global convergence to stationary points of ALM in both cases. 相似文献
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研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理. 相似文献
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We consider a nondifferentiable convex multiobjective optimization problem whose feasible set is defined by affine equality constraints, convex inequality constraints, and an abstract convex set constraint. We obtain Fritz John and Kuhn–Tucker necessary and sufficient conditions for ε-Pareto optimality via a max function. We also provide some relations among ε-Pareto solutions for such a problem and approximate solutions for several associated scalar problems. 相似文献
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We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with
explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach
extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured
convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection
from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems. 相似文献
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We present several equivalent conditions for the Karush–Kuhn–Tucker conditions for weak? compact convex sets. Using them, we extend several existing theorems of the alternative in terms of weak? compact convex sets. Such extensions allow us to express the KKT conditions and hence necessary optimality conditions for more general nonsmooth optimization problems with inequality and equality constraints. Furthermore, several new equivalent optimality conditions for optimization problems with inequality constraints are obtained. 相似文献
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P. L. Combettes 《Applied Mathematics and Optimization》1997,35(3):311-330
The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is
considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated
to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to
control the order in which the sets are selected. Weak and strong convergence results are established within thisbroad framework,
which provides a unified view of projection methods for solving hilbertian convex feasibility problems.
This work was supported by the National Science Foundation under Grant MIP-9308609. 相似文献